SOLUTION: the parallel sides of a trapezoid are of length 3 and 6cm. if the third side measures 5cm and the last side is perpendicular to the first two, what is the area of the trapezoid?

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Question 970248: the parallel sides of a trapezoid are of length 3 and 6cm. if the third side measures 5cm and the last side is perpendicular to the first two, what is the area of the trapezoid?
Answer by macston(5194) About Me  (Show Source):
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A right triangle is formed with the third side as hypotenuse(=5cm), the difference between the two bases as one leg(a=6cm-3cm=3cm) And the height of the trapezoid as the other leg (b):
.
a%5E2%2Bb%5E2=c%5E2
.
b=sqrt%28c%5E2-a%5E2%29
.
b=sqrt%28%285cm%29%5E2-%283cm%29%5E2%29
.
b=sqrt%2825cm%5E2-9cm%5E2%29
.
b=sqrt%2816cm%5E2%29
.
b=4cm The height of the trapezoid is 4 centimeters.
.
Area of trapezoid:
y=longer base; x=shorter base; h=height; A=area
.
A=%28%28x%2By%29%2F2%29h
A=%28%283cm%2B6cm%29%2F2%294cm
A=%289cm%2F2%29%284cm%29
A=%284.5cm%29%284cm%29
A=18cm%5E2
.
ANSWER: The area of the trapezoid is 18 square centimeters.